Abstract
A Moser-Trudinger inequality (with sharp constant) is proven for convolution type potentials defined on stratified groups. When combined with a new representation formula for functions defined on the Heisenberg group (which is based on explicit fundamental solutions to a class of singular or degen- erate subelliptic diVerential operators) we obtain the following Moser-Trudinger inequality with sharp constant on the Heisen- berg group H n .L et ⁄ H n be an open subset of H n with finite volume. Then sup
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